Will a spayed female try to mate?

  Will she have the need to mate with any dog? I notice my dog is attracted to our trainer's dog n so is he .... they could just be 2 friendly dogs that want to sniff butts lol .... but both of them cry when we dont let them ..... primarily my question is if my dog even tho she is spayed and does not go through heat feels the need to mate ?.... My family n I have had dogs before but they have never been neutered or spayed so I couldn't get an accurate answer from them.
It depends upon how long ago the dog was spayed. The hormones remain for several months after spaying so they could still react.

Sniffing rear ends is natural behavior and how dogs greet each other, spayed or intact.Smelling butts is nothing to do with mating as is mounting. Mounting can be play behavior but it can also be a dominance behavior. If your dogs are just sniffing rear ends, they are doing nothing more than what happens when you shake hands. It's proper dog greeting and not sexual at all.
No she will not want to mate ........ bum sniffing is social positive behaviour by dogs, they learns lots of information about each other by doing this, many owners stop dogs doing this however it is not negative dog behaviour
No, not at all. Once the ovaries and hormones are gone she will no longer have a biological urge to reproduce.
No a female will not mate and cannot mate without being in heat.
no
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they just like each other